Finite difference approximate solutions for the strongly damped extensible beam equations
Applied Mathematics and Computation
Finite element Galerkin solutions for the strongly damped extensible beam equations
The Korean Journal of Computational & Applied Mathematics
Existence results and numerical solutions for a beam equation with nonlinear boundary conditions
Applied Numerical Mathematics - Special issue: 2nd international workshop on numerical linear algebra, numerical methods for partial differential equations and optimization
Crowd dynamics on a moving platform: Mathematical modelling and application to lively footbridges
Mathematical and Computer Modelling: An International Journal
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This work is focused on the longtime behavior of a nonlinear evolution problem describing the vibrations of an extensible elastic homogeneous beam resting on a viscoelastic foundation with stiffness k0 and positive damping constant. Buckling of solutions occurs as the axial load exceeds the first critical value, @b"c, which turns out to increase piecewise-linearly with k. Under hinged boundary conditions and for a general axial load P, the existence of a global attractor, along with its characterization, is proved by exploiting a previous result on the extensible viscoelastic beam. As P@?@b"c, the stability of the straight position is shown for all values of k. But, unlike the case with null stiffness, the exponential decay of the related energy is proved if P